The radius of the orbit of an electron in a Hydrogen-like atom is $45 a_0$, where $a_0$ is the Bohr radius. Its orbital angular momentum is $\frac{3 h}{2 \pi}$. It is given that $h$ is Planck constant and $R$ is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are)

The ratio of minimum wavelengths of Balmer and Paschen series of hydrogen atom will be

The activity of a radioactive sample is measured as No counts per minute at $$t=0$$ and $$\mathrm{N}_0 / \mathrm{e}$$ counts per minute at $$t=6 \mathrm{~min}$$. The time (in minutes) at which the activity reduces to half its value is.

The wavelength of $$k_\alpha$$-line characteristic $$X$$-rays emitted by an element is $$0.32 \mathop A\limits^o$$. The wavelength of the $$k_\beta$$-line emitted by the same element will be